用一组判别式对两个二次曲面的相交曲线进行拓扑分类

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Computer Aided Geometric Design Pub Date : 2023-10-10 DOI:10.1016/j.cagd.2023.102244

Wenbing Shao, Falai Chen

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引用次数: 0

摘要

计算两个二次曲面的交线是计算机辅助设计系统中的一个基本问题，其中QSIC的拓扑分析是实现鲁棒计算的重要任务。本文提出了一种新的方法，利用与两个二次曲面相关的一组判别式对三维投影空间中QSIC的拓扑进行分类。新的拓扑分类方法给出了显式表示，即使当两个二次曲面的系数包含符号时也可以应用。提供了一些例子来说明新分类方法的使用。

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Topological classification of the intersection curves of two quadrics using a set of discriminants

Computing the intersection curves of two quadrics (QSIC) is a fundamental problem in computer aided design system, where the topology analysis of the QSIC is an essential task to realize the robust computation. In this paper, a new method is proposed to classify the topology of the QSIC in three dimensional projective space by using a set of discriminants associated with the two quadrics. The new topology classification method presents explicit representations and can be applied even when the coefficients of the two quadrics contain symbols. Some examples are provided to illustrate the usage of the new classification method.

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来源期刊

Computer Aided Geometric Design 工程技术-计算机：软件工程

CiteScore

3.50

自引率

13.30%

发文量

审稿时长

60 days

期刊介绍： The journal Computer Aided Geometric Design is for researchers, scholars, and software developers dealing with mathematical and computational methods for the description of geometric objects as they arise in areas ranging from CAD/CAM to robotics and scientific visualization. The journal publishes original research papers, survey papers and with quick editorial decisions short communications of at most 3 pages. The primary objects of interest are curves, surfaces, and volumes such as splines (NURBS), meshes, subdivision surfaces as well as algorithms to generate, analyze, and manipulate them. This journal will report on new developments in CAGD and its applications, including but not restricted to the following: -Mathematical and Geometric Foundations- Curve, Surface, and Volume generation- CAGD applications in Numerical Analysis, Computational Geometry, Computer Graphics, or Computer Vision- Industrial, medical, and scientific applications. The aim is to collect and disseminate information on computer aided design in one journal. To provide the user community with methods and algorithms for representing curves and surfaces. To illustrate computer aided geometric design by means of interesting applications. To combine curve and surface methods with computer graphics. To explain scientific phenomena by means of computer graphics. To concentrate on the interaction between theory and application. To expose unsolved problems of the practice. To develop new methods in computer aided geometry.

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